Fine-Grained System Identification of Nonlinear Neural Circuits
This addresses the challenge of fine-grained neural circuit identification in neuroscience, representing an incremental methodological advance.
The paper tackles the problem of recovering sparse nonlinear models of biological neural circuits from measurement data, establishing that a sign constraint on weights is necessary for system recovery and demonstrating this both theoretically and empirically on simulated circuits and mouse retina data.
We study the problem of sparse nonlinear model recovery of high dimensional compositional functions. Our study is motivated by emerging opportunities in neuroscience to recover fine-grained models of biological neural circuits using collected measurement data. Guided by available domain knowledge in neuroscience, we explore conditions under which one can recover the underlying biological circuit that generated the training data. Our results suggest insights of both theoretical and practical interests. Most notably, we find that a sign constraint on the weights is a necessary condition for system recovery, which we establish both theoretically with an identifiability guarantee and empirically on simulated biological circuits. We conclude with a case study on retinal ganglion cell circuits using data collected from mouse retina, showcasing the practical potential of this approach.